Meanwhile,
many engineering devices can be modeled as nonsmooth dynamical systems,
which deserve considerable attentions, and one can refer to [1]} and references therein. In general, the theory of the smooth dynamical system cannot be directly applied to the discontinuous case. In fact, when the vector field of (REF ) is discontinuous, there may be
grazing solutions, sliding solutions or impact solutions. Thus, we must study the discontinuous dynamic systems in theory and applications.
The analysis shows that system (REF ) has no sliding solutions. Therefore, how to extend Theorem A (Zhang [2]} smooth system) to the discontinuous case is an important problem. In this paper, we present more general results that can be applied to
the discontinuous Liénard system.
